Lord Justice Leveson's long-awaited report into press standards is set to be published amid fears its recommendations could throw the Government into turmoil.

The 2,000-page document is due to be unveiled at 1.30pm, with the judge widely expected to suggest a new newspaper regulator underpinned by law.

David Cameron set up the Leveson Inquiry in July last year in response to revelations that the News of the World commissioned a private detective to hack murdered schoolgirl Milly Dowler's phone after she disappeared in 2002.

The probe, set to cost around £6 million overall, heard months of dramatic evidence from celebrities, media figures, politicians and the police.

The Prime Minister on Wednesday pledged to seek cross-party consensus on a new regulatory system, but faces an uphill struggle to overcome deep divisions in the coalition and among his own MPs.

Mr Cameron is due to respond to the report in the Commons on Thursday afternoon - but the Liberal Democrats have already suggested Nick Clegg could make a separate statement.

The Deputy Prime Minister is reportedly ready to support the rapid creation of a regulator with statutory underpinning, a move that would be opposed by many Tories, and Mr Cameron is thought to be resisting. The pair have been poring over the report trying to agree a joint approach since half-a-dozen advance copies were delivered to Downing Street on Wednesday morning.

Asked about press regulation as he took questions in the Commons, Mr Cameron said: "This Government set up Leveson because of unacceptable practices in parts of the media and because of a failed regulatory system. I think we should try and work across party lines on this issue, it is right to meet with other party leaders about this issue and I will do so."

Labour former home secretary David Blunkett told the BBC Radio 4 Today programme the idea that the Press could emulate the judiciary by being embedded in statute but remaining independent was "bizarre". He urged people to "take a step back" from the report and not rush into changes, saying there was widespread agreement about the outcomes people wanted.

But Tory backbencher George Eustice argued that some kind of legal underpinning was required. He said: "We need to have accountability for the media as well as accountability for everyone else. I don't buy this argument that it would be the thin end of the wedge. It has not happened in broadcasting, and we have had broadcasting Acts since we have had broadcasting, effectively."